(Q11).In the adjacent figure, the height of a solid cylinder is 10 cm and diameter 7 cm. Two equal conical holes of radius 3 cm and height 4 cm are cut off as shown in the figure. Find the volume of the remaining solid.

10 cm4 cm3 cm

Volume of the remaining solid = Volume of the given solid – Total volume of the two conical holes

Radius of the given cylinder (r) =
d
2
 =
= cm

Height of the cylinder (h) = cm

Volume of the cylinder (V) = πr2h

=
× × ×
=

= cm3.

Radius of each conical hole, ‘r’ = cm

Height of the conical hole, h = cm

Volume of each conical hole,

V =
1
3
 πr2h =
×
× × ×
=
=
Total volume of two conical holes = 2 ×
=
cm3

Hence, the remaining volume of the solid

= -
=
× −
=
2695 - 528
7
 =

= cm3